Asymmetry and Hopf bifurcation in spherical Couette flow

Abstract

Spherical Couette flow is studied with a view to elucidating the transitions between various axisymmetric steady-state flow configurations. A stable, equatorially asymmetric state discovered by Bühler [Acta Mech. 81, 3 (1990)] consists of two Taylor vortices, one slightly larger than the other and straddling the equator. By adapting a pseudospectral time-stepping formulation to enable stable and unstable steady states to be computed (by Newton’s method) and linear stability analysis to be conducted (by Arnoldi’s method), the bifurcation-theoretic genesis of the asymmetric state is analyzed. It is found that the asymmetric branch originates from a pitchfork bifurcation; its stabilization, however, occurs via a subsequent subcritical Hopf bifurcation.